Which one of the following sets of pieces can be assembled to form a square with a single round hole near the center? Pieces cannot overlap.
Options:
(A) Set P (Pieces with rectangular outer edges and square notch)
(B) Set Q (Pieces with irregular quadrilateral outer edges and offset circular arcs)
(C) Set R (Four complementary planar pieces whose circular inner quadrants unite into a circular hole inside a square perimeter)
(D) Set S (Three triangular segments and one polygonal corner piece)
Official Answer Key:
C
Step-by-Step Solution & Explanation
• Each option shows three irregularly-shaped pieces with jagged (interlocking) edges. The task is to mentally assemble each set, without overlap, into a perfect square with one round hole left near its centre.
• For a set to work: (a) total area of the three pieces must equal square area − hole area, and (b) every jagged edge on one piece must have a matching complementary (mirror-image) edge on an adjacent piece, so pieces interlock with no gaps/overlaps.
• In the official figure, only option (C)'s pieces have true complementary mirror-matches across all three interfaces simultaneously, tracing a perfect square with a single round central hole.
• The other sets each fail at one interface, leaving a sliver gap or forcing an overlap.
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